library(readr)
package 㤼㸱readr㤼㸲 was built under R version 4.0.5replacing previous import 㤼㸱lifecycle::last_warnings㤼㸲 by 㤼㸱rlang::last_warnings㤼㸲 when loading 㤼㸱hms㤼㸲replacing previous import 㤼㸱lifecycle::last_warnings㤼㸲 by 㤼㸱rlang::last_warnings㤼㸲 when loading 㤼㸱tibble㤼㸲replacing previous import 㤼㸱lifecycle::last_warnings㤼㸲 by 㤼㸱rlang::last_warnings㤼㸲 when loading 㤼㸱pillar㤼㸲
library(ggplot2)
library(dplyr)
package 㤼㸱dplyr㤼㸲 was built under R version 4.0.5
library(rms)
package 㤼㸱rms㤼㸲 was built under R version 4.0.5package 㤼㸱Hmisc㤼㸲 was built under R version 4.0.5package 㤼㸱SparseM㤼㸲 was built under R version 4.0.4
library(synthpop)
package 㤼㸱synthpop㤼㸲 was built under R version 4.0.5
library(tidyr)
package 㤼㸱tidyr㤼㸲 was built under R version 4.0.5
library(plotly)
package 㤼㸱plotly㤼㸲 was built under R version 4.0.5
library(sjPlot)
package 㤼㸱sjPlot㤼㸲 was built under R version 4.0.5
library(performance)
package 㤼㸱performance㤼㸲 was built under R version 4.0.5
# install the 'mi' package if you are planning on redoing imputation on the original dataset. For now the imputed dataset has already been saved
# library(mi)
source('./helper functions.R')

Reading in original dataset, performing multiple imputation and writing out imputed dataset. This chunk commented out because we’ve already done this and saved the resulting file as our starting point.

Read in dataset from Brinati paper. Dataset already been imputed based on code above.


brinati_covid_study_v2.imputed <- read_csv("data/brinati-covid_study_v2_imputed.csv",
  col_types = cols(GENDER = col_factor(levels = c("M",
  "F")), SWAB = col_factor(levels = c("0",
  "1"))))

glm.orig.fit<-glm(SWAB ~ ., brinati_covid_study_v2.imputed, family='binomial')
glm.fit: fitted probabilities numerically 0 or 1 occurred
glm.orig.fit

Call:  glm(formula = SWAB ~ ., family = "binomial", data = brinati_covid_study_v2.imputed)

Coefficients:
(Intercept)      GENDERF          AGE          WBC    Platelets  Neutrophils  Lymphocytes    Monocytes  Eosinophils    Basophils          CRP          AST          ALT          ALP          GGT          LDH  
 -2.185e+00   -8.505e-01    1.746e-02   -1.146e-01    2.011e-03   -1.289e-01    9.374e-03    8.215e-01   -1.095e-08   -4.520e+00    5.427e-04   -7.082e-03    1.026e-02   -1.195e-02    5.287e-03    1.001e-02  

Degrees of Freedom: 278 Total (i.e. Null);  263 Residual
Null Deviance:      366.4 
Residual Deviance: 239.4    AIC: 271.4
write.csv(summary(glm.orig.fit)$coef, file='output/OR-original-model.csv', row.names = FALSE)
predicted = plogis(predict(glm.orig.fit))
observed = brinati_covid_study_v2.imputed$SWAB
assessPerf(predicted, observed)
          Dxy       C (ROC)            R2             D      D:Chi-sq           D:p             U      U:Chi-sq           U:p             Q         Brier     Intercept         Slope          Emax           E90          Eavg           S:z           S:p 
 7.322477e-01  8.661239e-01  5.000567e-01  4.514185e-01  1.269458e+02            NA -7.168459e-03  8.242296e-13  1.000000e+00  4.585870e-01  1.361516e-01 -2.780966e-08  1.000000e+00  6.627578e-02  5.261796e-02  2.628540e-02 -2.750989e-01  7.832403e-01 
p<-plot_model(glm.orig.fit)
p<-ApplyFigureThemeLargeFontOnly(p + ylim(.1, 2.5) ) 
Scale for 'y' is already present. Adding another scale for 'y', which will replace the existing scale.
  
p
ggsave(filename = 'figs/OR-original-model.png', plot=p, width=6, height=6, units='in', dpi=300)

Draw ROC curve

cms.cutoffs <- lapply(seq(0.01,0.99,0.01), function(cutoff) {
  ret=confusionMatrix(predicted, observed, cutoff=cutoff)
  ret$cutoff = cutoff
  ret
  })
ff<-data.frame(t(sapply(cms.cutoffs, function(cf) c("Cutoff"=cf$cutoff, "Sensitivty"=cf$sens, "Specificity"=cf$spec))))
colnames(ff) <- c('Cutoff', 'Sensitivity','Specificity')


cutoffs_to_plot <- c(0.09, 0.3, 0.6, 0.9)
p <- ApplyFigureTheme(ff %>% mutate(fpr=1-Specificity) %>% filter(Cutoff %in% cutoffs_to_plot) %>%
  ggplot(., aes(x=fpr, y=Sensitivity)) + 
    geom_point(size=3, color='darkblue') + xlim(0,1) + ylim(0,1)+
    xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  )
ggsave(filename = 'figs/example-sens-spec-on-roc.png', plot=p, width=6, height=6, units='in', dpi=300)

for (cutoff in lapply(1:length(cutoffs_to_plot), function(i) cutoffs_to_plot[1:i])) {
  p <- ApplyFigureTheme(ff %>% mutate(fpr=1-Specificity) %>% filter(Cutoff %in% cutoff) %>%
    ggplot(., aes(x=fpr, y=Sensitivity)) + 
      geom_point(size=3, color='darkblue') + xlim(0,1) + ylim(0,1)+
      xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  )
  ggsave(filename = paste0('figs/example-sens-spec-on-roc-', cutoff[length(cutoff)],  '.png'), 
         plot=p, width=6, height=6, units='in', dpi=300)
}
p <- ApplyFigureTheme(
  ggplot(ff, aes(x=1-Specificity, y=Sensitivity)) + geom_line()+ 
    geom_ribbon(aes(ymin = 0, ymax=Sensitivity), color=NA, fill='blue',alpha=0.3) + 
    xlim(0,1) + ylim(0,1)+
      xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)') 
)
ggsave(filename = 'figs/example-roc.png', 
         plot=p, width=6, height=6, units='in', dpi=300)
p <- ff %>% mutate(fpr=1-Specificity) %>%
  ggplot(., aes(x=fpr, y=Sensitivity)) + geom_point(aes(frame=Cutoff)) +
    xlab('False Positive Rate (1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  
  
ggplotly(p)

Draw calibration

```r
cal_breaks = seq(0, 1, .1)
cal_deciles <- data.frame(Predicted=predicted, Observed = as.integer(as.character(observed))) %>%
  mutate(Bins = cut(Predicted, breaks=cal_breaks, include.lowest = TRUE))
cal_deciles_summary <- cal_deciles %>% group_by(Bins) %>% summarise(n=n(), Average_Observed = mean(Observed),
                                                                    Average_Predicted=mean(Predicted)) 


for (cutoff in lapply(1:nrow(cal_deciles_summary), function(i) cal_deciles_summary$Bins[1:i])) {
  p<-ApplyFigureThemeCalCurvePoints(
    ggplot(cal_deciles_summary %>% filter(Bins %in% cutoff), aes(x=Average_Predicted, y=Average_Observed)) )
  p<-ApplyFigureThemeLargeFontOnly(p)
  SaveStdSquareFigure(p, filename = paste0('figs/example-cal-curve-points-', cutoff[length(cutoff)],  '.png'))
}

p<-ApplyFigureThemeCalCurvePoints(ggplot(cal_deciles_summary , aes(x=Average_Predicted, y=Average_Observed)) )
p<-ApplyFigureThemeLargeFontOnly(p)

SaveStdSquareFigure(p, 'figs/cal-curve-deciles-all.png')

p<-p + geom_smooth(method='lm', se=FALSE)
SaveStdSquareFigure(p, 'figs/cal-curve-deciles-all-with-bestfit.png')
p

<!-- rnb-source-end -->

<!-- rnb-plot-begin -->

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" />

<!-- rnb-plot-end -->

<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuTkFcbmBgYFxuYGBgIn0= -->

```r
```r
NA

<!-- rnb-source-end -->

<!-- rnb-chunk-end -->


<!-- rnb-text-begin -->


Calculate hosmer lemeshow statistics

<!-- rnb-text-end -->


<!-- rnb-chunk-begin -->


<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxuXG5obC5vcmcgPC0gcGVyZm9ybWFuY2VfaG9zbWVyKGdsbS5vcmlnLmZpdClcbmhsLm9yZ1xuYGBgXG5gYGAifQ== -->

```r
```r

hl.org <- performance_hosmer(glm.orig.fit)
hl.org

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Hosmer-Lemeshow Goodness-of-Fit Test

Chi-squared: 5.333 df: 8
p-value: 0.722 Summary: model seems to fit well.




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Create smoothed cal curve from Van hoorde et al

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```r
```r
p<-CreateSmoothedCalCurvePlot(predicted, observed)
p<-ApplyFigureThemeLargeFontOnly(p)
SaveStdSquareFigure(p, 'figs/smoothed-cal-curve-orig-data.png')
p

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<img 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IaTuokO3pNvnaoADe1VWh68LuzWP7jV//MdTvImGnh/7eOwB8DLY9ep/p//cJI3Uee8V46lKEb2Ki0OXmd2dfBy0E2sT4Ka6NIGpwmysb1KS4PXHl1zzetpdIOEk4GJbuR13Np0aK/SwuD1wK6u/p+R3UDh5GCinufdb4pzL0t61wOvVcH24V21sckEusHCycJEPfL+Y3Nz7eSrUigiSJFFwXbFk2q8+n8Bw8nDxDDPi/KtdPELtqvYVdT/4w67fsLJxATw+jAZcWfHrmxih24yfRLBRJ02/OH3RwlbTN+9Hd0y7jhvEB99YB3wjrijsjt8j1z/L2g42ZjoFuao1IIqTUR025PU8I4/sAp4h9xZsyvX/9OzGzacfEz08I629a9uXXw43Mk3MPbCdlCKD6wB3gF3ZHQVi3c7Ewd00+iTOCY6eBXb+t9uuuFV2G/6RthSR/EBwMthl1L/L3g4GZlo4FVt679rf94JvD5cCTmC4gMrgHcwaLqw29f/07EbIZycTDQ3KVTb+t+0P+6FtOD+8tEPr4ri/J3mA8uHVx40yeyqf3NtHnYjhJOViRpe1bb+ZUbbsHm7OcLbbyf5Uv2BxcMrDZqu7Jrr/8UIJy8T3TzveFv/+8s2Q2hT21rV5tMfqgc1y98NP/BlpbnrzAUWp1pfK0M1wKemAoBzh5qg9KvKSPDu2oH5pkx3VR9Y+Mgr/8V3HHeN9f+ihJObycTIK2zrr4S3U5Xmrg9e6S8+GV09u/r6f1HCyc5Em/OOtvVX5rydKl5Xl/NKeJHg1bNrrP8XJ5z8TNTwKrf1V802HL9QDrYrm22QAaPAa0RXW/8vUjgZmmjmeVXb+iumcfvBtuZ1XfO8A8QI8E4MuxqTSOHkaKK7w6bY1l91h+2m4bWE+OXa7rCx4dWxa67/FyucHE0MC3OG2/qXhJ4P1zaU+cWLT4e7V/WchOIDy4V3CNkkvBp2zfX/ooWTpYl5VdlnKbltM+GT9nZaPebuxMxY+oBkz2wVWbP18QjCCXh1l2rm+n/RwsnTRJs2/PZj9SSb/CibuFy3hbfOL05efBp/QLJntoqsufp4TKEZXg27E/X/ooWTqYkG3l2ZBzTjqNsz8AuFV4HnNLxKdE31/6KFk6uJdmHOo483HqoILhNeFZ5GeEnD7sAkXjjZmmhvUvzlny6L4vEv/4rC2SMp+TTBqxp3p+r/xQsnXxPd7eHv66uv75X3ghlaIrxqQA3wKtidrP8XL5yMTTTwNqsh66VigFeWhlAtvKprtcn6f/HCydlEC+/DVb0mByPvQDpGdfAq2J2u/xcvnKxNlPCW4H5XZQ0vDw83yHkl6djVwTtm1/SYz3pqoXgx0V6w1TcbqseAMNsgigkvZ9htTaKGk7eJGt5mA4Yn7nudLg1eLXZqeJXDrt6jMokaTuYmmpsUd6+KatHC/eW52z6964Z3yO7kdqXX27jhZG5iXtvw8IvybbqWBa+ZOxK7Jos1VaHyYmKG11lrhnfALqUkShbIpGOihffun968eeNcEmhR8JoHTTO7pCJqeSCTjokh523KCLoVVlkSvGbwhvCO2Z1Cd5sJMumYmGYbmmcpMNvQaIK8AbwSu6j/F8bEMM/79ZvXWFXWawo9GV6RXWrZ1ajhLMJEd4et+IsqX3i4KXCHrdYkexK8Q3an0d3GDWcZJpq1DUW/fwi29a80DZ8Ir8AuEd1t3HAWYqIbeVtkS4wx8h6Y8B7ZJWYMKywb7MVEnfPuupF3Xwgb9FpoIfAS8DvC27NLRncbOZylmKjhbR5iPxzuLh1LYS4DXgp/PbwSuyR0t5HDWYzJCN7711XlwE1dQrD679d/s/q0gQRgB2/HLh3dbeRwlmMyhleswYY6bAdqMfdriV16xrDSgu1eTADvlAkRweshu8TvbSOHsySTEbxSAcFBEUG+8oeXyuD1kV0OutvI4SzKRLO2wZeyh5cM4XX3yA8nYxiuPc8CmXRMAK/RhAxhBy9v2N1GDmdhJhp47/7tzZs3//xh9HGu1gRvxS4P3W3scBZmooT351+1F2tffOd45MzhZXBYVfk5dWQ3D2TSMVHB+16Ya3jhduT1wNuyy/jGNno4SzNRwLuTZsqcVkRmDi+L3dNTV3QzQSYdkzG81W4jJ99W82Off7cpXG8Pz11nzkWcyoCnp6f6+n8oChhGY3h3ArDNtjku8Bp+l/rIyxl3S3ZZw+42fjgLNBnfpLiSKwCtdkkkg8QS3VNO1XfA68dEdXtYyBTWuxidzuGzil1O1Xctu3kgk46JCl4BV9f9nrKFl8fuGafqu57dPJBJxwTwKk3o6Jbs1mtxOPBGD2ehJsqc91gkcL/OnJeObscuB97o4SzVZDzbID4wXK2PXOFjQBx2u+cm6PBGD2exJmN4y8G2eNysaqj3zfle8S2ylgxvdS/4+KwlGd744SzWZAxvlTcUxclfvfnrTbNJr4uyhJeMrsAuGd744SzXRHF7+P6VcHd4hfvzktmV9hYhwhs/nAWbqBbmPLzt2XXcZy9HeMnoyvuR0eCNH86STVTwVvubfrUpTr76W+cFvfnBS0R3yC4N3vjhLNpEDa83ZQcvkd3taO9oCrzxw1m2CeCVTMjojvbsJ8AbP5yFmwBe0YSErpJdArzxw1m6CeAVTMjoKuqrTcE7QziLNwG8RxMKu1sNu4B3BhPA25uQ0VWxOwVv/HBWYAJ4O5NpdE3sTsAbP5w1mADe1mSa3e5nJbtmeOOHswoTwNuYkNHVsGuEN3446zABvLXJFLqT7BrgnSGclZgA3spkil0JXSW7enhnCGctJoD3cDD9xR9s4KRlVwtv/HDWYwJ4TX/xh9uV6tnVmUQPZ00mgNcArwJdHbsak/jhrMlk9fDqB83hlo9GdtUm8cNZlcna4dVyN9rg3Myu0iR+OOsyWTm8Wu5GO+2a0VWZzBDOykzWDa+Ou/Em0VPsAt4ZTFYNr4Y7RUmUSXbH8MYPZ3UmK4ZXx51ib/5pdkfwRg9nhSbrhVfDnaqsBIHdIbzRw1mjCQveu+qZ+OfyI8U/vy6Kk/a9rnrmcW++ZOHVcKcsokZhdwBv7HDWacKBt2VT2ui/Lb5yUm8KdbvJBF4dd8pqPiR2ZXgjh7NWEwa8D1fVHmZ3V+K+kfvi5LtD9V7N6360OVSa8Gq4UxeiorErwhs7nNWaMOC93dSEluNvv/deyXNdAqB972ZUwCJJeNXcacquEtkV4I0dznpNGPDu2nF1d0T0/rLNIWpsH65GpYMShFfDnab+H5XdHt7Y4azZhAHvTTvi7hX7Tdfw3l8++uFVUZwLBKcHr5o7A7o0djt4Y4ezahM6vGWK0MB7uxnB24zA3fWakDwkB6+SO22hdjq7Lbyxw1m3CR3ePkVoc19Ru3ow3te7Un9+285HfFlp7jpzstTl/J4+1dT/q9hFXcB05QXefYPrrs0nbo6TDmmNvMoh89mzp5r6f4xxtx55Y4ezehMf8O43J9Le/0JSnBK8GnRLeD2wW8IbORyY+Mh5d8P6xALdCcGrQ/eZej0v41qtgddDNHkgk46J82zDw/tRbe0U4VUC116nqeDlsrvN4mwvzMRtnrcej7uyFf3QnF7aYEJXCS+X3UzO9sJM3O6wHR5uhGG4vVDrbruJ9sxWkUXz0KHbXqiN4GUPu56igQnPhLe24Xy4tmEnvrjdFC8+VcXb0lqYo8RNnNkdwmvDbh5ne2EmnFVl7U2IJsWth9luDWRbr21XDJedzQ/vJLojePkpg69oYMIz4cArreet4d0XEryHu2px7wvhcm5ueLXoilO7Mrw2w66naGDCM2HBy9e88KppG90LluC1ZDePs70wk+XCq4FNsYxBhNcqZfAVDUx4JkuF14Du6GawAK81u3mc7YWZLBNeHWzq1WNHeHnseo8GJjyTBcKrhU238LGH14HdPM72wkyWB68JXfXysQ5eFrshooEJz2Rh8Oph06Lbwcub3g0SDUx4JouC1wrdFl4Wu4GigQnPZDnwGljTZwwdvI7DrqdoYMIzWQq8JtbM6Fbwug67nqKBCc9kCfCaWZtCt4TXA7t5nO2FmeQO7xRqExlDJR/oZnK2F2aSObxTtdan0fXEbh5ne2EmOcO7nSpXTUCXxa6pMVmc7YWZZAtvg9NU/T8Su1PDN4XdPM72wkyyhPfIk4E7+rBLg3eiTVmc7YWZZAevTBS1/p+JXRq8U+3K4mwvzCQreMdIGer/kdmlwDvdtizO9sJMsoFXDZWaOxa6FHgJ7cvibC/MJAd4DVSR6v9NsDsJL6mRWZzthZmkD6+RK3X9P+Kw282QTcBLa2YWZ3thJknDO8kgpf7fFLoT8FIjzeJsL8wkUXinsVVyx8gYhBsTBnjpkWZxthdmkiK8VHKH3Nmha4KXEWkWZ3thJqnBywB3wJ1VxmCGlxNpFmd7YSapwMuEdsyd7bCrh5cXaRZne2EmScBrSa7AnQO6OniZkWZxthdmMju89uAeuaNlDNoFZCp42ZFmcbYXZjInvE7YCtw5DbtbBbw2kWZxthdmkj+8ruiO4bWKNIuzvTCT3OHlZAy6NecyvJaRZnG2F2aSObxP3dGV4bWONIuzvTCT0PCaChhyiksqpS1dKalBl+YYqXQj5EUZj7yG+n+MYVcceV0izWKoWphJvvDq6//x0EXB9mxNcoXXUP+PiS4Ktmdrkie8/RyDCd6zMxq7tYlzpFmc7YWZZAmvof4fH13UvM7WJEN4TfX/LNBF2eBsTbKDV74roYaXQ+42kxMFk7Fyg9dY/09il2h4yOREwWSsvOA11/8TyGXtPpbFiYLJWDnBq1jHoC7Yztw4L4sTBZOxMoJ3ov7fEV1ysts1xEekMIlvkg28U/X/uAnDVmiIj0hhEt8kE3h1Kx/l4pVkdgcN8REpTOKb5AEvqf6fJbqZnCiYjJUDvOb6f2dnLHK3iob4iBQm8U3Sh9f4rMSZO7qZnCiYjJU6vOHRzeREwWSsxOE1oMvkVotuJicKJmMlDa8eXT65W0NDfEQKk/gmCcOryxjEZIFayGdramQWJwomY6ULrxLdM5HcLbEWytRS8yxOFEzGShXeCXS7d1DIZ80macKrzBhUaS5qoazZJEl4x+jqLtBQC2XNJgnCK6F7Jmn0WezIv2aT5OA9ZgxnZxPkmuDlNDKLEwWTsVKDt0OXAK4BXl4jszhRMBkrLXgrdGnU6uHlNzKLEwWTsVKC97QSb70CttZds0kS8DasyugSyJXhtW9kFicKJmPNDm8Ha48ujVoZXrdGZnGiYDLWnPAKGUKdMbCwbeH10cgsThRMxkoDXtre/EMdMuljmAQyYcF797Yoiucf9O+NPjAN75ZaEmVMrjkyumCSqQkH3vvLotLJO9174w8QLtiIJVFkaAmR0QWTTE0Y8D5cFY8/HO7K/35Sv6f4wDS8VHTZkdEFk0xNGPDebh59PNTD6/fq9xQfmILXjO50m7LoY5gEMmHAuyuetP9/qX5P8QEzvIqMYboZsgfz8zBZkgkD3pt2QN0LaYH0nuIDRngvSk0f1qgs+hgmgUzo8JYZbcPm7aZnU3pP9QEDvBffOKObSR/DJJAJHd77y3YWoU1tR+8NP/BlJV39t28qRaw3By1QAeEV/20MVWUMPv5dZjFAwCSQySzwNsku4IWJm8kMOe9Fe6EGeGHiZhJ9tuGin2MAvDBxM4k9zytMjwFemLiZxL3DJs3sAl6YuJnw1jacK9Y2nItrG4YfkOC9kO9KAF6YuJkw4C1HVmHR2E2TI0jvSS8k+0rDG2qAFyZuJhx4peW6Lbzk9bzje8GAFyZuJix4+ersLxTrGAAvTNxM4sCrXIIDeGHiZhIDXs3qMcALEzeT8PCqMoZagBcmbibB4dUv2gW8MHEzCQ2vYb054IWJm0loeCEonMLCawQ7/iHVSqYhaIlChJYA3hSElowFeI1KpiFoiUJpwgtBfgR4oWwFeKFsBXihbAV4oWwVGF7+zr4RG/Lz66I4ad9rd2kt+of3Y7ZEPnisLhkf6OGq6FQ1JV6fHKqDPTG0Tt0nYeG12Nk3XkPeN6fmpH7wrn0YJPyJUrVEOnisLlEcaABvtD6p1D3koGydpk+Cwmuzs2+0huyLk+8O1Xv1udkP+i5mS6SDx+oS04FuNzUmsfqkasxNIR+MhElQeG2eO47VkLJD6gf12/duhOf6I7dEPnisLjEcqOuaWH1SDiGvigG8JEyCwmuz40OshvSbVNWn6OEq/J9pXUvkg8fqEsOBds0IF61PyiG+ePGTDC8Jk6Dw2uy1E60hx9+9rFB+9EP5r/88+NlStUQ6eKwu0R+oG+Ci9clhf/7jMEchYRISXqtdzmI1pFMzAnfXJqGHO2VLxIPH6hLDgW5aRGL1SSMZXhomIeG12iVd53IAAAOESURBVF8yVkM6NX8jyz9c5SXB57ehL/KVLREPHqtL9AfqM8tYfXJojybCS8Nk7fDum1PTpnmjCZsoLREPPj+8XWui9UkjwMtoSKP95kS6gA2daRojrg4+O7zdVIPcrJAt6Y6SFrzp57y74Z/E0MgYI64OPnvOO+6B0H3SKLWcN/XZhof3o3Qu+IkyRVwffO7Zht0oSZgD3vlnG5Ke5202t/zY/xgJGUVL5IPPPc/b35mI1yftURKb5035Dlt1R1L8e1B3zzjhi9ES6eAz32Hr88uIfVJrAO/8d9hsdvaN1pCd+OJ2U7z4VN2lDP0XUtUS6eCxukRzICFHiNYntQbwkjAJu6rMYmffWA3p1vu1N9V3RaS1XKoukQ4eq0uULZFyhGh90hy4hZeBScT1vLSdfWM1ZN+z2zTrrlrc+yJCcqfsEvHgs6znVcEbr08OY3jnX88LQQEFeKFsBXihbAV4oWwFeKFsBXihbAV4oWwFeKFsBXihbAV4/aq/cXfy9Y/Tn652+agf/1Tdg3343b9MfG/tArx+Jdx1JuBlgvfnV/p1ZYC3FuD1KxHe6UWNBnirhUOA1yzA61f7dmuvz++He8CoZIAQ8E4L8PpVB2/NV/1gRPHyfzbVctTD/wqbUtbLpE6+/b/ByHv3dlMUX3z7qVpb1S94039v7QK8ftXDW+FX/lTC+1XR/VRfyNXD6b5ZoHr+SoK3fbd5bKuD1/C9tQvw+pVi5K30a2Ea4p20El6A9/jukyO8pu+tXYDXr/qc9+1x3HzyqWe52g6xfbd5xEaEt3z35Mf6k6VFm/Mav7d2AV6/EmcbOiCrjOB202YGFYsVkf2zLj283VXY7Vff/rG/YDN+b+0CvH4lwFtnqbuiea5GeL/eWaRhT5oqk+cX2lfG761dgNeveti+aOYHFPCevOsxZcE7/t7aBXj9aj8o4SDAe3yfN/Lqv7d2AV6/0sFbZaniNiOGnPf+N8//S8x59d9buwCvX+ngrecQPhzaS65u1uByNNvwXbWDWsWrMNug/d7aBXj9Sgcvb563/Erz4vEnzPPqBXj9Sgtvd7uiga7bAuZXyjts9YublmLD99YuwOtXenjrgpvF1+IahecfblRrG5o9ah7ettvV6L+3dgFeKFsBXihbAV4oWwFeKFsBXihbAV4oWwFeKFsBXihbAV4oWwFeKFsBXihbAV4oW/0/nt0TFl7BSv0AAAAASUVORK5CYII=" />

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Boot strap performance in the original dataset

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<img src="data:image/png;base64,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" />

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# Assess performance in external validation

II. Look at performance as a function of prevalence

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```r
```r
prevalences = seq(0.01, 0.99, 0.01)
brinati.syn.factory = generateSyntheticDataFactory(baseDF = brinati_covid_study_v2.imputed, method = 'boot')
dfs_prevs <- lapply(prevalences, function (prev) brinati.syn.factory(prev = prev))
dfs.prevs.perf <- lapply(dfs_prevs, function(df) {
  assessPerf(predicted = plogis(predict(glm.orig.fit, newdata=as.data.frame(df))), observed = df$SWAB)
})

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Calculate the different validation measures

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```r
```r

dfs.prevs.perf.df <- data.frame(matrix(unlist(dfs.prevs.perf), nrow = length(prevalences), byrow = TRUE))
colnames(dfs.prevs.perf.df) <- names(dfs.prevs.perf[[1]])
dfs.prevs.perf.df$Prevalence = prevalences
dfs.prevs.perf.df <- gather(dfs.prevs.perf.df, Measure, Value, Dxy:`S:p`, factor_key = TRUE)

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Plot the distribution of validation measures

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```r
```r
measures = c('C (ROC)', 'Brier', 'Intercept', 'Slope')
p<-ggplot(dfs.prevs.perf.df %>% filter(Measure %in% measures), aes(x=Measure, y=Value,  color=Measure)) + geom_boxplot() +
  geom_point(data=data.frame(Measure = measures, Value = c(1, 0, 0, 1)), size=3, color='blue') + theme_bw()
p<-ApplyFigureThemeLargeFontOnly(p)
SaveMedRectFigure(p, 'figs/change-in-metrics-due-to-prevalence-boxplot.png')
p
p<-ggplot(dfs.prevs.perf.df %>% filter(Measure %in% measures), aes(x=Prevalence, y=Value,  color=Measure, group=Measure)) + geom_line(size=1.3) + theme_bw()
p<-ApplyFigureThemeLargeFontOnly(p)
SaveMedRectFigure(p, 'figs/change-in-metrics-due-to-prevalence-linearplot.png')

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/>

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<!-- rnb-source-begin eyJkYXRhIjoiYGBgclxuYGBgclxucFxuYGBgXG5gYGAifQ== -->

```r
```r
p

```

Calculate Decision Curve

---
title: "R Notebook"
output: html_notebook
---
```{r message=FALSE}
library(readr)
library(ggplot2)
library(dplyr)
library(rms)
library(synthpop)
library(tidyr)
library(plotly)
library(sjPlot)
library(performance)
# install the 'mi' package if you are planning on redoing imputation on the original dataset. For now the imputed dataset has already been saved
# library(mi)
source('./helper functions.R')
```

Reading in original dataset, performing multiple imputation and writing out imputed dataset. This chunk commented out because we've already done this and saved the resulting file as our starting point.
```{r echo=FALSE, warning=FALSE}
# 
# brinati_covid_study_v2 <- read_csv("data/brinati-covid_study_v2.csv",
# col_types = cols(GENDER = col_factor(levels = c("M",
# "F")), SWAB = col_factor(levels = c("0",
# "1"))))
# brinati_covid_study_v2 <- brinati_covid_study_v2 %>% mutate_if(is.numeric, .funs = function(x) {x+0.001})
# brainati.mi <- missing_data.frame(as.data.frame(brinati_covid_study_v2), favor_positive = TRUE)
# 
# 
# brainati.mi<-change(brainati.mi, y=c('Lymphocytes', 'Basophils', 'Monocytes','Eosinophils', 'Basophils'), what='type', to='positive-continuous')
# show(brainati.mi)
# image(brainati.mi)
# 
# options(mc.cores = 4)
# imputations <- mi(brainati.mi, n.iter = 90, n.chains = 4, max.minutes = 20) 
# show(imputations)
# round(mipply(imputations, mean, to.matrix = TRUE), 3)
# Rhats(imputations)
# dfs <- complete(imputations, m=2)
# brinati_covid_v2.imputed <- dfs[[1]][,1:16]
# write.csv(brinati_covid_v2.imputed, file='./data/brinati-covid_study_v2_imputed.csv', row.names = FALSE)
```

Read in dataset from Brinati paper. Dataset already been imputed based on code above. 
```{r}

brinati_covid_study_v2.imputed <- read_csv("data/brinati-covid_study_v2_imputed.csv",
  col_types = cols(GENDER = col_factor(levels = c("M",
  "F")), SWAB = col_factor(levels = c("0",
  "1"))))
```


```{r}

glm.orig.fit<-glm(SWAB ~ ., brinati_covid_study_v2.imputed, family='binomial')
glm.orig.fit
write.csv(summary(glm.orig.fit)$coef, file='output/OR-original-model.csv', row.names = FALSE)
predicted = plogis(predict(glm.orig.fit))
observed = brinati_covid_study_v2.imputed$SWAB
assessPerf(predicted, observed)
p<-plot_model(glm.orig.fit)
p<-ApplyFigureThemeLargeFontOnly(p + ylim(.1, 2.5) ) 
  
p
ggsave(filename = 'figs/OR-original-model.png', plot=p, width=6, height=6, units='in', dpi=300)
```

# Draw ROC curve
```{r}
cms.cutoffs <- lapply(seq(0.01,0.99,0.01), function(cutoff) {
  ret=confusionMatrix(predicted, observed, cutoff=cutoff)
  ret$cutoff = cutoff
  ret
  })
ff<-data.frame(t(sapply(cms.cutoffs, function(cf) c("Cutoff"=cf$cutoff, "Sensitivty"=cf$sens, "Specificity"=cf$spec))))
colnames(ff) <- c('Cutoff', 'Sensitivity','Specificity')


cutoffs_to_plot <- c(0.09, 0.3, 0.6, 0.9)
p <- ApplyFigureTheme(ff %>% mutate(fpr=1-Specificity) %>% filter(Cutoff %in% cutoffs_to_plot) %>%
  ggplot(., aes(x=fpr, y=Sensitivity)) + 
    geom_point(size=3, color='darkblue') + xlim(0,1) + ylim(0,1)+
    xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  )
ggsave(filename = 'figs/example-sens-spec-on-roc.png', plot=p, width=6, height=6, units='in', dpi=300)

for (cutoff in lapply(1:length(cutoffs_to_plot), function(i) cutoffs_to_plot[1:i])) {
  p <- ApplyFigureTheme(ff %>% mutate(fpr=1-Specificity) %>% filter(Cutoff %in% cutoff) %>%
    ggplot(., aes(x=fpr, y=Sensitivity)) + 
      geom_point(size=3, color='darkblue') + xlim(0,1) + ylim(0,1)+
      xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  )
  ggsave(filename = paste0('figs/example-sens-spec-on-roc-', cutoff[length(cutoff)],  '.png'), 
         plot=p, width=6, height=6, units='in', dpi=300)
}
p <- ApplyFigureTheme(
  ggplot(ff, aes(x=1-Specificity, y=Sensitivity)) + geom_line()+ 
    geom_ribbon(aes(ymin = 0, ymax=Sensitivity), color=NA, fill='blue',alpha=0.3) + 
    xlim(0,1) + ylim(0,1)+
      xlab('False Positive Rate\n(1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)') 
)
ggsave(filename = 'figs/example-roc.png', 
         plot=p, width=6, height=6, units='in', dpi=300)
p <- ff %>% mutate(fpr=1-Specificity) %>%
  ggplot(., aes(x=fpr, y=Sensitivity)) + geom_point(aes(frame=Cutoff)) +
    xlab('False Positive Rate (1-Specificity)') + ylab('True Positive Rate\n(Sensitivity)')
  
  
ggplotly(p)
```

# Draw calibration
```{r}
cal_breaks = seq(0, 1, .1)
cal_deciles <- data.frame(Predicted=predicted, Observed = as.integer(as.character(observed))) %>%
  mutate(Bins = cut(Predicted, breaks=cal_breaks, include.lowest = TRUE))
cal_deciles_summary <- cal_deciles %>% group_by(Bins) %>% summarise(n=n(), Average_Observed = mean(Observed),
                                                                    Average_Predicted=mean(Predicted)) 


for (cutoff in lapply(1:nrow(cal_deciles_summary), function(i) cal_deciles_summary$Bins[1:i])) {
  p<-ApplyFigureThemeCalCurvePoints(
    ggplot(cal_deciles_summary %>% filter(Bins %in% cutoff), aes(x=Average_Predicted, y=Average_Observed)) )
  p<-ApplyFigureThemeLargeFontOnly(p)
  SaveStdSquareFigure(p, filename = paste0('figs/example-cal-curve-points-', cutoff[length(cutoff)],  '.png'))
}

p<-ApplyFigureThemeCalCurvePoints(ggplot(cal_deciles_summary , aes(x=Average_Predicted, y=Average_Observed)) )
p<-ApplyFigureThemeLargeFontOnly(p)

SaveStdSquareFigure(p, 'figs/cal-curve-deciles-all.png')

p<-p + geom_smooth(method='lm', se=FALSE)
SaveStdSquareFigure(p, 'figs/cal-curve-deciles-all-with-bestfit.png')
p
            
```

Calculate hosmer lemeshow statistics
```{r}

hl.org <- performance_hosmer(glm.orig.fit)
hl.org
```

Create smoothed cal curve from Van hoorde et al
```{r}
p<-CreateSmoothedCalCurvePlot(predicted, observed)
p<-ApplyFigureThemeLargeFontOnly(p)
SaveStdSquareFigure(p, 'figs/smoothed-cal-curve-orig-data.png')
p
```

Boot strap performance in the original dataset
```{r warning=FALSE, echo=FALSE}
df <- as.data.frame(brinati_covid_study_v2.imputed)
nBoot = 100
set.seed(1342349)
trainIdxBoot <- lapply(1:nBoot, function(i) sample(1:nrow(df), size=nrow(df), replace=TRUE))

bootPerf.origdata <- lapply(trainIdxBoot, 
                   function(trainIdx) 
                     assessSingleTrainTest(trainIdx, (1:nrow(df))[-trainIdx], df, glm.model = SWAB~ ., outcome.var.name = 'SWAB')
                   ) 

measures = c('C (ROC)', 'Brier', 'Intercept', 'Slope')
brinati.orig.boot.perf <- data.frame(matrix(
  unlist(lapply(bootPerf.origdata, function(boot) boot$test.perf)), 
  nrow = nBoot, byrow = TRUE))
colnames(brinati.orig.boot.perf) <- names(bootPerf.origdata[[1]]$test.perf)

brinati.orig.boot.perf <- gather(brinati.orig.boot.perf, Measure, Value, Dxy:`S:p`, factor_key = TRUE)
p<-ggplot(brinati.orig.boot.perf %>% filter(Measure %in% measures), aes(x=Measure, y=Value,  color=Measure)) + geom_boxplot() +
  geom_point(data=data.frame(Measure = measures, Value = c(1, 0, 0, 1)), size=3, color='blue') + theme_bw()
p<-ApplyFigureTheme(p)
SaveStdSquareFigure(p, 'figs/orig-model-bootstrap-evaluation.png')
p
```

# Assess performance in external validation

II. Look at performance as a function of prevalence
```{r}
prevalences = seq(0.01, 0.99, 0.01)
brinati.syn.factory = generateSyntheticDataFactory(baseDF = brinati_covid_study_v2.imputed, method = 'boot')
dfs_prevs <- lapply(prevalences, function (prev) brinati.syn.factory(prev = prev))
dfs.prevs.perf <- lapply(dfs_prevs, function(df) {
  assessPerf(predicted = plogis(predict(glm.orig.fit, newdata=as.data.frame(df))), observed = df$SWAB)
})
```

Calculate the different validation measures
```{r}

dfs.prevs.perf.df <- data.frame(matrix(unlist(dfs.prevs.perf), nrow = length(prevalences), byrow = TRUE))
colnames(dfs.prevs.perf.df) <- names(dfs.prevs.perf[[1]])
dfs.prevs.perf.df$Prevalence = prevalences
dfs.prevs.perf.df <- gather(dfs.prevs.perf.df, Measure, Value, Dxy:`S:p`, factor_key = TRUE)
```

Plot the distribution of validation measures
```{r}
measures = c('C (ROC)', 'Brier', 'Intercept', 'Slope')
p<-ggplot(dfs.prevs.perf.df %>% filter(Measure %in% measures), aes(x=Measure, y=Value,  color=Measure)) + geom_boxplot() +
  geom_point(data=data.frame(Measure = measures, Value = c(1, 0, 0, 1)), size=3, color='blue') + theme_bw()
p<-ApplyFigureThemeLargeFontOnly(p)
SaveMedRectFigure(p, 'figs/change-in-metrics-due-to-prevalence-boxplot.png')
p
p<-ggplot(dfs.prevs.perf.df %>% filter(Measure %in% measures), aes(x=Prevalence, y=Value,  color=Measure, group=Measure)) + geom_line(size=1.3) + theme_bw()
p<-ApplyFigureThemeLargeFontOnly(p)
SaveMedRectFigure(p, 'figs/change-in-metrics-due-to-prevalence-linearplot.png')
p
```

# Calculate Decision Curve
```{r}
cms.cutoffs <- lapply(seq(0.01,0.99,0.01), function(cutoff) {
  ret=confusionMatrix(predicted, observed, cutoff=cutoff)
  ret$cutoff = cutoff
  ret
  })

calculate_net_benefit_at_threshold_for_sensitivity_and_specificity <- function(sens, spec, threshold) {
  sens - (1-spec)*(threshold/(1-threshold))
}
netbenefit_across_thresholds = sapply(cms.cutoffs, function(cutoff_values) calculate_net_benefit_at_threshold_for_sensitivity_and_specificity(cutoff_values$sens, cutoff_values$spec, cutoff_values$cutoff))
netbenefit_vs_thresholds = data.frame(thresholds = sapply(cms.cutoffs, function(cutoff_values) cutoff_values$cutoff), netbenefit = netbenefit_across_thresholds)
ggplot(netbenefit_vs_thresholds, aes(x=thresholds, y=netbenefit)) + geom_line() + ylab("Net Benefit") + xlab("Threshold to Act") + theme_bw()
```

